This seems super intuitive, but I can't seem to prove it. Is the set of equivalence classes of totally ordered sets totally ordered?
More precisely, given two totally ordered sets, $F$ and $G$, does there always exist an order preserving injection from one into the other?
I would think there is some adaptation of Zermelo's theorem that can fix the problem, but again, I can't seem to find it.
from Hot Weekly Questions - Mathematics Stack Exchange
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